Relaxing in foam

We investigate the mechanical response of an aqueous foam, and its relation to the microscopic rearrangement dynamics of the bubble-packing structure. At rest, even though the foam is coarsening, the rheology is demonstrated to be linear. Under flow, shear-induced rearrangements compete with coarsening-induced rearrangements. The macroscopic consequences are captured by a novel rheological method in which a step-strain is superposed on an otherwise steady flow

Effect of hydrogel particle additives on water-accessible pore structure of sandy soils: A custom pressure plate apparatus and capillary bundle model

To probe the effects of hydrogel particle additives on the water-accessible pore structure of sandy soils, we introduce a custom pressure plate method in which the volume of water expelled from a wet granular packing is measured as a function of applied pressure. Using a capillary bundle model, we show that the differential change in retained water per pressure increment is directly related to the cumulative cross-sectional area distribution $f(r)$ of the water-accessible pores with radii less than $r$. This is validated by measurements of water expelled from a model sandy soil composed of 2 mm diameter glass beads. In particular, the expelled water is found to depend dramatically on sample height and that analysis using the capillary bundle model gives the same pore size distribution for all samples. The distribution is found to be approximately log-normal, and the total cross-sectional area fraction of the accessible pore space is found to be $f_0=0.34$. We then report on how the pore distribution and total water-accessible area fraction are affected by superabsorbent hydrogel particle additives, uniformly mixed into a fixed-height sample at varying concentrations. Under both fixed volume and free swelling conditions, the total area fraction of water-accessible pore space in a packing decreases exponentially as the gel concentration increases. The size distribution of the pores is significantly modified by the swollen hydrogel particles, such that large pores are clogged while small pores are formed

Rain water transport and storage in a model sandy soil with hydrogel particle additives

We study rain water infiltration and drainage in a dry model sandy soil with superabsorbent hydrogel particle additives by measuring the mass of retained water for non-ponding rainfall using a self-built 3D laboratory set-up. In the pure model sandy soil, the retained water curve measurements indicate that instead of a stable horizontal wetting front that grows downward uniformly, a narrow fingered flow forms under the top layer of water-saturated soil. This rain water channelization phenomenon not only further reduces the available rain water in the plant root zone, but also affects the efficiency of soil additives, such as superabsorbent hydrogel particles. Our studies show that the shape of the retained water curve for a soil packing with hydrogel particle additives strongly depends on the location and the concentration of the hydrogel particles in the model sandy soil. By carefully choosing the particle size and distribution methods, we may use the swollen hydrogel particles to modify the soil pore structure, to clog or extend the water channels in sandy soils, or to build water reservoirs in the plant root zone

Topological persistence and dynamical heterogeneities near jamming

We introduce topological methods for quantifying spatially heterogeneous dynamics, and use these tools to analyze particle-tracking data for a quasi-two-dimensional granular system of air-fluidized beads on approach to jamming. In particular we define two overlap order parameters, which quantify the correlation between particle configurations at different times, based on a Voronoi construction and the persistence in the resulting cells and nearest neighbors. Temporal fluctuations in the decay of the persistent area and bond order parameters define two alternative dynamic four-point susceptibilities, XA(t) and XB(t), well-suited for characterizing spatially-heterogeneous dynamics. These are analogous to the standard four-point dynamic susceptibility X4(l,t), but where the space-dependence is fixed uniquely by topology rather than by discretionary choice of cutoff function. While these three susceptibilities yield characteristic time scales that are somewhat different, they give domain sizes for the dynamical heterogeneities that are in good agreement and that diverge on approach to jamming

The partition of energy for air-fluidized grains

The dynamics of one and two identical spheres rolling in a nearly-levitating upflow of air obey the Langevin Equation and the Fluctuation-Dissipation Relation [Ojha et al. Nature 427, 521 (2004) and Phys. Rev. E 71, 01631 (2005)]. To probe the range of validity of this statistical mechanical description, we perturb the original experiments in four ways. First, we break the circular symmetry of the confining potential by using a stadium-shaped trap, and find that the velocity distributions remain circularly symmetric. Second, we fluidize multiple spheres of different density, and find that all have the same effective temperature. Third, we fluidize two spheres of different size, and find that the thermal analogy progressively fails according to the size ratio. Fourth, we fluidize individual grains of aspherical shape, and find that the applicability of statistical mechanics depends on whether or not the grain chatters along its length, in the direction of airflow.Comment: experimen

The Hindered Settling Function at Low Re Has Two Branches

We analyze hindered settling speed versus volume fraction $\phi$ for dispersions of monodisperse spherical particles sedimenting under gravity, using data from 15 different studies drawn from the literature, as well as 12 measurements of our own. We discuss and analyze the results in terms of popular empirical forms for the hindered settling function, and compare to the known limiting behaviors. A significant finding is that the data fall onto two distinct branches, both of which are well-described by a hindered settling function of the Richardson-Zaki form $H(\phi)=(1-\phi)^n$ but with different exponents: $n=5.6\pm0.1$ for Brownian systems with P\'eclet number ${\rm Pe}<{\rm Pe}_c$, and $n=4.48\pm0.04$ for non-Brownian systems with ${\rm Pe}>{\rm Pe}_c$. The crossover P\'eclet number is ${\rm Pe}_c\approx10^8$, which is surprisingly large.Comment: Supplementary material available on reques

Dynamical heterogeneity in soft particle suspensions under shear

We present experimental measurements of dynamical heterogeneities in a dense system of microgel spheres, sheared at different rates and at different packing fractions in a microfluidic channel, and visualized with high speed digital video microscopy. A four-point dynamic susceptibility is deduced from video correlations, and is found to exhibit a peak that grows in height and shifts to longer times as the jamming transition is approached from two different directions. In particular, the time for particle-size root-mean square relative displacements is found to scale as $\tau^* \sim (\dot \gamma \Delta \phi^4)^{-1}$ where $\dot\gamma$ is the strain rate and $\Delta\phi=|\phi-\phi_c|$ is the distance from the random close packing volume fraction. The typical number of particles in a dynamical heterogeneity is deduced from the susceptibility peak height and found to scale as $n^* \sim (\dot \gamma \Delta \phi^4)^{-0.3}$. Exponent uncertainties are less than ten percent. We emphasize that the same power-law behavior is found at packing fractions above and below $\phi_c$. Thus, our results considerably extend a previous observation of $n^* \sim \dot\gamma^{-0.3}$ for granular heap flow at fixed packing below $\phi_c$. Furthermore, the implied result $n^*\sim (\tau^*)^{0.3}$ compares well with expectation from mode-coupling theory and with prior observations for driven granular systems